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Around the time of the French Revolution, Francisco de Goya began portraying kings as citizens. Soon after it, Jean-Auguste-Dominique Ingres began portraying citizens as kings. Not even photography would usher in a more radical change in humanity’s depiction of itself. With the giants of the 17th century, you know where you are: Velázquez paints Spanish imperialism, Rembrandt the Dutch bourgeoisie. The Enlightenment collapsed those barriers. Modernity, and its queasy tensions and dissatisfactions with the self, entered portraiture.

The line from Goya and Ingres, via Manet and Degas, to Warhol and Chuck Close, with their parodies of Identikit snapshots and 15-minute-fame democracy, is unbroken. No exhibition has unravelled the story before: the Royal Academy’s “Citizens and Kings, Portraits in the Age of Revolution 1760-1830” is an unprecedented, entertaining, intelligently conceived panorama of the epoch.

Art as spectacle is its post-modern theme, and it opens with a dazzling piece of theatre. As if a curtain were swept back on the centuries, you enter the lofty central Wohl gallery, with its red-gilt interior and neoclassical flourishes, to stand in the presence of half a dozen crowned heads of state, each a towering full-length figure swathed in a fantasy of crimson velvet, gold brocade and shimmering, speckled fur.

Some – Antoine-François Callet’s “Louis XVI”, Joshua Reynolds’ “George III”, Thomas Lawrence’s “George IV” – are as familiar as fact, remembered from schooldays as icons of pre-guillotine hubris, Georgian sobriety, Regency decadence. Others are virtuoso displays where personality emerges through bravura handling of paint and detail: the bony narrow face, creamy watered-silk cassock and soft, ribboned red slippers of Lawrence’s saintly “Pope Pius VII”. All are public relations exercises: most blatantly Vigilius Eriksen’s stately, unrelenting “Catherine the Great”, depicted – just after she had had her husband murdered and assumed the Russian throne – in a billowing, tent-like gold robe as a pyramid of power, in a portrait sent as a gift to Buckingham Palace and hastened straight into storage; this is its first public outing.

All these artists have a job to do; the drama comes when they are uneasy about doing it. Thus the electrifying juxtaposition here is Goya’s “Ferdinand VII in Royal Robes” alongside Ingres’ “Napoleon I on the Imperial Throne”. These are paintings first, history second; they live as art, not documents. Goya could not stand the idiotic Ferdinand, and against a neutral grey background – unheard of in a royal portrait – he depicts a stumpy, heavy-jawed, slothful brute whose plainness is strikingly at odds with the delicately handled imperial accessories. The material substance of paint creates the mood of disenchantment: all Goya’s flair goes into a depiction of fancy dress – Ferdinand’s cloak a sweeping expanse of red glinting against the brilliant green of his breeches; gold embroidery suggested by small, thick flecks of yellow, black, white, coalescing into an evocatively uncertain blur – whose power announces the ambivalence between the abstract symbols of monarchy and their embodiment in a man of flesh and blood.

Goya was an old man when he depicted Ferdinand. Ingres, 30 years younger, was unstirred by politics but very ambitious and, at the age of 26, painted “Napoleon” to make his name at the salon. It backfired. Everything disorientating about the work now – its flatness, the exaggerated head, fake skin colour, regressive Gothic style, with its play of references to the medieval emperor Charlemagne – was yet more shocking to Parisians in 1806, for it declared a contemporary truth in a most subversive, near-surreal, way. Ingres was a conservative, a history painter, but in finding his own distancing, hypnotic, difficult style, he turned Napoleon into an effigy, the monster of inhumanity and authoritarian power that he really – surreally – was.

Putting the giants Goya and Ingres in a broader European setting, the Royal Academy skilfully dramatises art’s inextricable link to politics. As late as 1781, Mozart was placed beneath the valet in the Archbishop of Salzburg’s household, but by 1812, Beethoven told Goethe, as the Empress of Austria and a train of dukes approached, “they must make way for us, not us for them”. Across 11 rooms and the work of almost 100 artists here, we watch ancien régime hierarchies dissolve before a new belief in individuality and genius. Voltaire, Rousseau, Benjamin Franklin and Madame de Stael parade before us: the first generation of philosophes whose likenesses we know as living, feeling, thinking beings.

Everything here dramatises the erosion of the history genre by the character portrait: from Anton Raphael Mengs’ sparkling teenage bride strolling with a parrot, “The Marquesa de Llano”, to Reynolds’ sour, fractious old lady walking her spaniel, “Mary, Countess of Bute”; from Gainsborough’s “Mrs Sheridan” and “The Byam Family”, bittersweet images of fleeting beauty in the English landscape, to Jacques-Louis David’s poignant portrait of the fallen revolutionary hero “General Gérard, Marshal of France”, an isolated actor on an empty stage still clinging to the grandeur of his neoclassical marble backcloth.

But it is in the work of Goya and Ingres above all that social revolution is embedded in formal and stylistic concerns, and the great painterly story of this exhibition is the march of these two artists to modernity. Goya’s cross-legged, impetuous “Ferdinand Guillemardet”, the obscure doctor who became the ambassador to Madrid of the young, victorious French Republic, is a masterpiece of the new naturalistic, introspective portraiture. Thirty years later, when Goya himself was a political exile in Bordeaux, his liberal sympathies shine through again more sadly, in penetrating, meditative portraits of fellow exiles such as the publisher “Joaquin Maria Ferrer”.

Ferrer shares the final room here with two other monumental portraits of the late 1820s and early 1830s: Ingre’s masterpiece “Louis-François Bertin”, and the only work in the show by Ingres’ up-and-coming young rival Delacroix, the National Gallery’s portrait of the dandy “Louis-Auguste Schwiter”. Though the Delacroix is warmed by the red of Schwiter’s hat, contrasted in turn with subtle shades of blue in the pottery planter at his feet, all three works are severe and direct in their overwhelming black and white tonality, compositionally simple – and point straight to Manet.

Yet Ingres looks back, too, to the rigidity and block-like primitivism of “Napoleon”. The massive, odd proportions – outsize head, claw-like hands – chiselled surfaces and casual virtuosity of “Louis-François Bertin” are all disconcerting. With a mordant expression, Bertin, a powerful editor, leans forward out of shallow space, his bulky body exaggerated so that it bulges from his clothes, his expressive eyes fixing you so resolutely that you wither under his gaze. The big-eyed society fright “The Comtesse de Tournon” in the centre of this show appeals and repulses in exactly the same way; both make a heroic virtue, as so often in Ingres, of awkwardness or ugliness.

Picasso for obvious reasons was obsessed with Ingres, but the psychological isolation of all Ingres’ figures here as vividly calls to mind Matisse, with his dictum about painting not things but the distance between them. Ingres hated his own time – “I want to break with my century. That is how ignorant, stupid and brutal I find it” – and set out to emulate the great history painters of the past. But in the end he painted his own alienation and constructed not historical but contemporary, bourgeois myths – Bertin with the formal grandeur of Napoleon, citizen as king – and so made real life the only subject of modern art. It is a fabulous, rarely explored story, put marvellously into context here.

‘Citizens and Kings, Portraits in the Age of Revolution 1760-1830’, Royal Academy, London W1, to April 20. Tel +44 (0)20 7300 8000